A $3$ GHz parallel polarization plane wave with a peak amplitude of $1$ V$/$m is propagating in free space at an unknown angle relative to the z$-$axis but in the $+$z$-$direction and $+$x$-$direction. This wave is incident on a lossless dielectric half space that begins at z $=0.$ If the transmitted wave propagates in the dielectric medium at an angle of $12$ with respect to the z$-$axis and the relative permittivity of the dielectric medium is $$r $=13\mathrm{.}5,$ answer the following questions.